Report

Refraction at plane surface and Prisms Dr. M K Raghavendra BASE, Bangalore Type 1 – Snell’s law and RI Snell’s law: 1 n2 sin(i ) sin(r ) c Absolute R I in terms n of speed of light v Modified Snell’s law n1 sin i1 n2 sin i2 V Y R nV nY nR 1 n2 Relative R I in terms of speed of light Relative R I in terms of absolute R I v1 v2 n2 1 n2 n1 Relative R I in terms of wavelength of light 1 n2 Frequency remains constant 1 2 1) A ray of light is incident on the interface of two media at an angle of 450 and is refracted in to the other medium at an angle of 300. If the speed of light in the first medium is 3X108ms-1 ,what is the speed of light in the second medium? (1) 1.96X108ms-1 (2) 2.12X108ms-1 (3) 3.18X108ms-1 (4) 3.33X108ms-1 Snell’s law: n sin(i ) sin(r ) sin 45 3X 10 8 sin 30 v 1/ 2 3X 10 8 1/2 v 3X 10 8 v 2.12 X 10 8 ms 1 2 c n v Thus sin(i ) c sin(r ) v In general sin i1 v1 sin i2 v2 2)A ray of light is travelling from medium A to medium B. The angle of incidence is i and that of refraction is r. Graph between sin(i) and sin(r) is as shown in Figure below. We can conclude the following (i) Speed of light in medium B is three-fourth of that in medium A. (ii) Total internal reflection cannot take place. (iii) Refractive index of medium B is greater than that of medium A. sin (r) O Correct conclusions are (1) Only (i) and (ii) (3) (i), (ii) and (iii) 370 sin (i) (2) Only (ii) and (iii) (4) Only (i) and (iii) sin r The slope of the straight line: tan sin i sin (r) sin (r) O 370 sin (i) sin (i) sin r vB 3 sin i v A 4 3 vB v A 4 sin r tan 37 0 sin i sin r 3 or sin i 4 Medium B is denser than medium A Since nb > na TIR cannot take place 3) Given refractive index of glass with respect to air is ang = 3/2 and that of water with respect to air is anw = 4/3, the refractive index of glass with respect to water is (1) 8/9 (2) 9/8 (3) 2 (4) 1/2 n1 1 n2 n2 a ng ng na ng and ng /na nw a nw na 3/2 9 w ng nw nw /na 4/3 8 Type 2: Normal Shift and Lateral Shift Lateral shift SL Normal shift a) Object in denser b) Object in rarer t sin( i r ) cos r 1 SN t(1 ) r nd SV SY SR r nd SN t(n 1) SV SY SR Re al depth Apparent depth r nd Apparent depth Real depth 4) A vessel of height h is filled with a liquid of refractive index n1 to a height h/2 and the upper half of the vessel is filled with a liquid of refractive index n2. The apparent depth of the vessel as seen along the normal is 1) n1 n 2 h n n 2 1 3) h n1 n 2 2 n1n 2 2) h 2 n1 n 2 n n 2 1 4) 2 h n1n 2 n n 2 1 In case of one liquid the apparent depth is given by In case of many layers of liquid A.D h /2 h /2 n1 n2 h n n1 = 2 2 n1 n2 ti A.D ni real depth refractive index 5) A ray of light passes through four transparent media with refractive indices 1 2 3 and 4 as shown in the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have (1) (2) (3) (4) 1= 2 2= 3 3= 4 4= 1 1 2 B A D 3 C 4 a sin ia b sin ib 1 sin i1 4 sin i4 Apply to medium 1 and medium 4 Since ray AB and CD are parallel, i1 and i4 are equal Implies 1 = 4 In genral a sin ia b sin ib c sin ic ............... 6) An ink dot on a paper placed on a table top is viewed from a distance of 30 cm above it with the help of a telescope. A 16 cm thick glass slab is placed on the ink dot. By what distance the telescope should be raised to refocus the ink dot ? The refractive index of glass is 1.6. (1) (2) (3) (4) 3 cm 4 cm 5 cm 6 cm The telescope should be moved up by a distance (y) equal to normal shift produced by the slab 1 Sn t 1 n 1 y Sn 16 1 6cm 1.6 7) Consider the situation shown in the figure. The bottom of the vessel is a plane mirror, S is a small fish located at a height of H/2 from the plane of the mirror, T is a human eye located at a height of H from the surface of water. The distances at which the fish sees the images of the eye (with respect to its position) are 1) T 1 3 H 2n aboveand H 2n below 2 2 2) 1 3 H 1 aboveand H 1 below 2n 2n 3) 1 3 H n aboveand H n below 2 2 4) 2 3 H 2 aboveand H 2 below 2n 2n H H S (H/2) Image 1 nH + H/2 T nH + H H Image 1: H (n+1/2) A.P = nH H S nH + H+H/2 ( H/2) Image 2: H (n+3/2) Image 2 Type 3: Critical angle and Total Internal Reflection nr sin C nd 1 sin C r nd nV nY nR CV CY C R vd sin C vr 8) A, B and C are three optical media of respective critical angles C1, C2 and C3. Total internal reflection of light can occur from A to B and also from B to C but not from C to A. Then the correct relation between critical angles is (1)C1>C2>C3 (2) C1= C2= C3 (3)C3> C1> C2 (4)C1<C2<C3 T I R can occur when light travels from medium A to medium B nA nB T I R can occur when light travels from medium B to medium C nB nC Therefore nA nB nC C1 C2 C3 9) What is the critical angle, C for calcite ( =1.5) immersed in oil ( =1.1)? (1) C tan11.1 1.5 (2) C cos11.1 1.5 (3) C sin 11.5 1.1 (4) C sin 11.1 1.5 nO 1 sin C nC O nC 1.1 sin C 1.5 Type 4: Prism, angle of deviation, minimum deviation d i1 i2 A A r1 r2 n AD 2 A sin 2 sin 10) The minimum angle of deviation for a prism of refractive index 1.732 is equal to its refracting angle. What is the angle of prism? (1) 400 (2) 450 (3) 600 (4) 300 In this case A = D AD sin( ) 2 n A sin( ) 2 A A sin( ) sin A 2 1.732 A A sin( ) sin 2 2 A A 2 sin cos sin A A 2 2 3 2 cos A A 2 sin sin 2 2 A/2 =300 3 A cos o 2 2 Or A=60 11) A ray of light is incident on one refracting face of a prism of angle 750. It passes through the prism and is incident on the other face at critical angle. If the refractive index of the material of the prism is √2, then the angle of incidence on the first face is (1) 300 (2) 450 (3) 600 (4) 75 0 sin C 1 1 n 2 We know that C = 450 r1 + C =750 r1 =300 750 r1 C sin i but n sin r sin i 2 0 sin 30 1 1 sin i 2 X 2 2 i 450 Type 5: Small angled prism , angular dispersion and dispersive power Deviation d A(n 1) Angular dispersion A(nV nR ) Dispersive power In case of C D F line angular dispersion nV nR nv nR mean deviation 1 2 nmean nF nC nD 2 12) The dispersive power of the material of the prism for which refractive index for violet and red colours are nv = 1.524, nr = 1.514 respectively is (1) (2) (3) (4) 0.025 0.034 0.019 0.015 Dispersive power is given by angular dispersion net deviation (nV nR ) nV nR 1 2 (1.524 1.514) 0.01 0.019 1.524 1.514 1 0.519 2 Type 6: Combination of Prisms Dispersion with out deviation A(nD 1) A(nD 1) A(nd 1)(1 Deviation with out dispersion ) A(nF nC ) A(nF nC ) d A(nD 1) A(nD 1) 13) A crown glass prism of 60 is cemented with a flint glass prism to form a pair which produces dispersion without deviation. If the refractive index of the crown glass prism is 1.52 and that of flint glass 1.66, then the angle of flint glass pair should be (1) 4.730 (2) 5.730 (3) 6.730 (4) 7.730 Condition for dispersion with out deviation is A1 (ny 1) A2 (ny1 1) 6(1.52 1) A2 (1.66 1) 6X 0.52 A2 4.72 0.66 Conceptual questions 14) Light appears to travel in straight line because (1)The frequency of light is very small (2) Light consists of very small particles (3) The wavelength of light is very small (4) The velocity of light is different for different colours. 15) When light is refracted through a prism, maximum deviation occurs when the following conditions are satisfied (i) the ray is incident grazing the first face (ii) the ray emerges out grazing its second face Options (1) Only in case (i) (3) In both the cases (2) Only in case (ii) (4) Not under these cases 16) A man is swimming underwater with undisturbed surface. Looking up at a bright sky through the water, he will see (1)a bright patch directly above whose angular size is independent of the depth of the swimmer (2)a shining surface of the water (3) just darkness (4) a bright patch directly above whose angular size depends upon the depth of the swimmer CC All the best Thank You